Multi-assets real options

Real options present a wide topic in investment litterature nowadays. However, despite big advances in the single asset investment pricing, the theory is miser of informations about problems involving more than one asset. We show in this paper that using dynamic programming, one can find an analytic trigger for a three assets simple exchange problem. Although we get a forward investment rule, one can not find the precise option value ex ante but only an average value. The precise option value depends on the first exit time from the continuation region which is stochastic. This is a quite intuitive effect of the course of dimensionality of the problem. Valuating a single asset project gives a single condition for the optimal decision rule. The same holds for the simple exchange problem with two assets since the value of the project just depends on the price over cost ratio. In a three assets problem, as the project don't depend anymore of a single state variable, one can't region.